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Page 1: Introduction to Hyperbolic Geometry by Amber Case | Ignite Portland 8

An Introduction to Hyperbolic Geometry

By Amber CaseCyborg Anthropologist

Ignite Portland 8Twitter: @caseorganic

Page 2: Introduction to Hyperbolic Geometry by Amber Case | Ignite Portland 8

M. C. Escher

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Euclid, 300 B. C.

Once upon a time…

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5 Postulates

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The 5th Postulate…

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János Bolyai

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v

Lobachevsky Gauss Klein

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ALWAYS 180°!

Less than 180°!

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The Spherical Triangle!

270°!

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Riemann

HyperbolicManifolds

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1997: Daina Taimina, Cornell

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Page 15: Introduction to Hyperbolic Geometry by Amber Case | Ignite Portland 8

Ancient City Model

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Present Day

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Page 19: Introduction to Hyperbolic Geometry by Amber Case | Ignite Portland 8

Page 20: Introduction to Hyperbolic Geometry by Amber Case | Ignite Portland 8

Thank You!

CyborgCamp October 2010

Cyborgcamp. com Twitter: @caseorganic

caseorganic@gmail. com

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